Expert: Abe Mantell - 8/27/2010

Question

Use the Rational Roots Theorem to solve for the rational roots

3x4 - 2x3 + 8x2 - 6x - 3 = 0  

Answer
I gather you meant: 3x^4 - 2x^3 + 8x^2 - 6x - 3 = 0
So, the rational root theorem states that *if* there are
rational roots to this polynomila, then it would have to be
of the form (factors of -3)/(factors of 3)
thus, possible roots: x = {-1, 1, -3, 3}/{-1, 1, -3, 3}
or -1, 1, -3, 3, -1/3, or 1/3

You can try each one, and you'll see that x=1 and x=-1/3 are the
only rational roots (the other two are imaginary: -sqrt(3)i, sqrt(3)i).

Abe